BIAS IN LINEAR MODEL POWER AND SAMPLE SIZE DUE TO ESTIMATING VARIANCE

Area of Science:

• Statistics
• Biostatistics
• Quantitative Psychology

Background:

• Sample size calculations for the General Linear Univariate Model typically rely on variance estimates from prior studies.
• These estimates, along with noncentrality, power, and sample size, are subject to inherent randomness.
• Censoring of variance estimates introduces additional complexity, impacting the accuracy of these calculations.

Purpose of the Study:

• To develop methods for computing the distribution function, moments, and quantiles of censored variance estimates.
• To provide accurate calculations for estimated noncentrality, power, and sample size in the presence of censored data.
• To assess and mitigate potential bias introduced by ignoring censoring in statistical analyses.

Main Methods:

• Derivation of simple expressions for computing censored variance estimates, noncentrality, power, and sample size.
• Development of convenient approximations for these statistical measures.
• Evaluation of the accuracy of the derived expressions and approximations.

Main Results:

• Demonstrated that ignoring right censoring falsely widens confidence intervals for noncentrality and power.
• Showed that ignoring left censoring falsely narrows confidence intervals for noncentrality and power.
• Quantified the potentially substantial bias introduced by censoring in statistical planning.

Conclusions:

• The developed methods allow for straightforward computation of key statistical parameters even with censored variance estimates.
• Accurate assessment and avoidance of bias caused by censoring are crucial for reliable study planning.
• The findings provide essential tools for researchers using the General Linear Univariate Model to ensure valid sample size and power calculations.